ISSN:0024-6107    

DOI:10.1112/jlms/54.2.209

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Suppose thatWis a countable ℵ0‐categorical structure. We investigate the question as to whether every finite cover ofW splits, that is, has an expansion which is a trivial finite cover ofW. We show that for most primitive structuresWwhich are homogeneous for a single binary relation (homogeneous graphs, partial orderings, the Henson digraphs, …) any finite cover splits. However, in contrast to this, we show that there are non‐split covers (with finite kernels) of the countable, universal, homogeneous local order.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.210

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

It is known that there are only finitely many normal CM‐fields with class number one or with given class number (see [9, Theorem 2;11, Theorem 2]) and J. Hoffstein showed that the degree of any normal CM‐field with class number one is less than 436 (see [2, Corollary 2]). Moreover, K. Yamamura has determined all the abelian CM‐fields with class number one: there are 172 non‐isomorphic such number fields. In a recent paper the author and R. Okazaki moved on to the determination of non‐abelian but normal octic CM‐fields with class number one. Noticing that their class numbers are always even, they got rid of quaternion octic CM‐fields, then they focussed on dihedral octic CM‐fields and proved that there are 17 dihedral octic CM‐fields with class number one.The aim of this paper is to get back to the quaternion case: we shall show that there exists exactly one quaternion octic CM‐field with class number 2, namely: Q(√α) with α = −(2 + √2)(3 + √3). Moreover, we shall show that the Hilbert class field of this number field is a normal and non‐abelian CM‐field of degree 16 with class number one.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.227

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.239

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we give an oscillation criterion for the quasi‐differential equation (py′)′ +qy= 0. The results include a generalisation of an oscillation theorem of Hartman. We also give a necessary and sufficient condition for oscillation.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.251

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

IfGis a word hyperbolic group of cohomological dimension 2, then every subgroup ofGof typeFP2is also word hyperbolic. Isoperimetric inequalities are defined for groups of typeFP2and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an application to ‘relative hyperbolicity’. Finitely presented subgroups of Lyndon's small cancellation groups of hyperbolic type are word hyperbolic. Finitely presented subgroups of hyperbolic 1‐relator groups are hyperbolic. Finitely presented subgroups of free Burnside groups are finite in the stable range.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.261

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We give a new proof of Aronson's upper gaussian bound on the heat kernel for parabolic equations with time‐independent real measurable coefficients. This approach also gives gaussian bounds in the case of a complex perturbation of real coefficients and in the case of uniformly continuous and complex‐valued coefficients.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.284

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this work, we study three, by now classical, operators from the point of view of their weak type (1,1) behaviour with respect to weights. The first one is the Bochner‐Riesz multiplier operator of index12(n− 1). We show that it is of weak type (1,1) with respect to any weight in theA1‐Muckenhoupt class.The other two are the maximal operator and the homogeneous singular integral (the former in any dimension and the latter in dimension 2) with rough kernel. We prove that they are of weak‐type (1,1) with respect to weights(ω,[ℳ~(ωβ)]1/β)for β>1, whereℳ~is a composition of the Hardy‐Littlewood maximal operator and the maximal operator with rough kernel.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.297

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we study weighted norm inequalities for the commutators [b,Sn] wherebis a BMO function andSndenotes thenth partial sum of the Fourier series relative to a system of orthogonal polynomials on [−1, 1] with respect to general weights. Results about generalized Jacobi and Bessel Fourier series are obtained.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.311

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A simple criterion for the involutivity of a system of partial differential equations of polynomial type is proved. The criterion involves the equations themselves and does not require the system to be in orthonomic form. It is proved that a system of partial differential equations is involutive if it is a differential Gröbner basis with respect to a total degree ordering, and if the compatibility conditions of the symbol equations of the system consist of equations of degree one. An algorithm for calculating these compatibility conditions is given.

ISSN:0024-6107    

DOI:10.1112/jlms/54.2.323

出版商:Oxford University Press    

年代:2016

数据来源: WILEY